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Solve the following system of equations by computing the inverse of the coefficient matrix

INSTRUCTIONS TO CANDIDATES
ANSWER ALL QUESTIONS

In your Written report, give the detailed answers to questions 1, 2, and 3. In your Video report, present in full detail the answer to question 3.

 

1. Consider the linear system (where  and  are constants):

x + 3y + z =  2x + y + z = 1 2x + 3y + 4z = 3

Find conditions on  and/or  such that:

(a) The system has a unique solution.

(b) The system has no solution.

(c) The system has infinitely many solutions.

 

 

 

2. Solve the following system of equations by computing the inverse of the coefficient matrix

No credit will be given for solutions obtained by any other method.

2x  4 y = 3

– 3x + 6 y + 4z = 6

x + 2 y  2z = 0

 

 

 

3. Consider the matrix

 

 

 

  1 0

 

 5 2 .

 

(a) Find elementary matrices E1 and E2 such that E2E1A = I.

(b) Use part (a) to write A-1 as a product of elementary matrices.

 

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